Fact one: up to 50,000 students and lecturers marched through the streets of London in yesterday's protest against government plans to triple tuition fees and slash government teaching grants in higher education. Fact two: a few hundred protesters – at most – broke away and attacked the building that houses Conservative party HQ, did some damage, caused some injuries, generated some striking images, and eventually got involved in a stand-off with police, who were taken by surprise. Fact three: the two protests, the larger peaceful one and the smaller violent one, will inescapably have become tangled in the reporting and public perception of yesterday's events. Fact four: tangled or not, these were politically significant events for Britain and should be taken seriously.

They should be taken seriously because, in spite of a reprehensible violent sideshow, this was a large protest with significant public support and the capacity to have a palpable impact on mainstream politics. You do not have to believe that the country's students and lecturers are the most downtrodden victims of the coalition's spending cuts – there may be better candidates for that accolade in Iain Duncan Smith's welfare reform announcements today – to recognise that they may be a lightning rod for wider public unease with the government's public spending strategy. But the fact that students and lecturers are so concentrated in particular parliamentary constituencies, plus the fact that the Liberal Democrats hold many of these seats, gives the higher education protesters a particular and unusual purchase. Most of what happened yesterday is likely to weaken the resolve of Lib Dem MPs to support the tuition fee plans when the vote comes.

Yesterday may — but only may — also mark a bigger tipping point. Public opinion remains in flux about the cuts. The popular belief that the deficit must be tackled coexists with anxiety that the cuts are too deep and rapid. That tension has not yet been resolved one way or the other. Yet the size of yesterday's protests is likely to encourage opponents of other parts of George Osborne's package to match the students' effort. That does not mean that every protest will command equal public support, or deserve to do so. Public support for strikes is selective and support for violence non-existent. In the end, the mood may harden against the protests. But the public is capable of making a distinction between a well-supported good cause and a small number of provocateurs. Intelligently conducted, the protests retain lots of potential to command the wider support in the political centre that they need to succeed and thus to cause headaches, and perhaps even second thoughts, for anxious ministers.